Multi-session Network Coding characterization using new linear coding frameworks
Recently, Network Coding (NC) has emerged as a promising technique in modern communication networks and has shown extensive potentials in practical implementations and theoretical developments. Nevertheless, the NC problem itself remains largely open especially where the multiple flows (sessions) exist. Unlike single-session where all receivers want the same information, they demand different set of information in multi-session and thus NC strategy should be carefully designed to avoid interferences. However, characterizing an optimal strategy (even a simple solution) has known to be of prohibitive complexity even we restrict to the linear network coding (LNC) problem. This thesis provides a fundamental approach to overcome this multi-session complexity. We first consider the Directed Acyclic Integer-Capacity network model that characterizes the real-life instantaneous Wireline Networks . In this model, people recently applied the results of wireless interference channels to evade the multi-session difficulties. However, our NC understanding is still nascent due to different wireline channel characteristics to that of wireless. Therefore, motivated by the graph-theoretic characterizations of classic linear NC results, we first propose a new Precoding-based Framework and its fundamental properties that can bridge between the point-to-point network channel and the underlying graph structures. Such relationships turn out to be critical when characterizing graph-theoretically the feasibility of the Precoding-based solutions. One application of our results is to answer the conjecture of the 3-unicast interference alignment technique and the corresponding graph-theoretic characterization conditions. For Wireless Networks, we use the packet erasure network model that characterizes the real-life harsh wireless environment by the probabilistic arguments. In this model, we consider the multi-session capacity characterization problem. Due to the signal fading and the wireless broadcasting nature, the linear NC designer needs to optimize the following three considerations all together: LNC encoding operations; scheduling between nodes; and the feedback and packet reception probabilities. As a result, the problem itself is more convoluted than that of wireline networks where we only need to focus on how to mix packets, i.e., coding choices, and thus our understandings have been limited on characterizing optimal/near-optimal LNC strategies of simple network settings. To circumvent the intrinsic hardness, we have developed a framework, termed Space-based Framework, that exploits the inherent linear structure of the LNC problem and that can directly compute the LP(Linear Programming)-based LNC capacity outer bound. Motivated by this framework, this thesis fully characterizes more complex/larger network settings: The Shannon capacity region of the 3-node network with arbitrary traffic patterns; and The LNC capacity region of the 2-flow smart repeater network.
Wang, Purdue University.
Information Technology|Electrical engineering
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